The three Ps: simple tools for monitoring economic cycles - pronounced, pervasive and persistent economic indicators

Business Economics, Oct, 1999 by Anirvan Banerji

The Statistics Corner usually discusses some set of data - what they represent, how they are collected and their strengths and weaknesses. In this column, we turn to the issue of how to tease some information out of highly volatile time series, and especially, how we can determine cyclical turning points. Our guest columnist, Anirvan Banerji, has much experience in looking for turning points. Working with Dr. Geoffrey Moore, one of the pioneers in business cycle research, he has undertaken numerous consulting assignments helping corporations analyze where their markets are headed. He also is the creator of a number of leading indicators used by economists today.

- Maurine Haver, Editor, The Statistics Corner

A key task for a business economist monitoring the economy is the assessment of the significance of changes in cyclical economic indicators. It is often important to tell whether movements in economic indicators are mostly attributable to noise, or are signaling a genuine shift in direction.

While cyclical economic indicators may have a long-term trend component, they certainly have a cyclical component and an irregular component, i.e., noise. A simple but useful way to tell cyclical signals from noise is to look at the indicators in terms of their "three Ps" - by checking whether the movements are Pronounced. Pervasive and Persistent.

This is not entirely a new idea. It is inherent in the notion of the three Ds (Duration, Depth and Diffusion), which have long been the standard criteria for measuring the severity of a recession (Fabricant, 1972). However, while the three Ds apply only to cyclical downturns, the three Ps apply to both upturns and downturns as a tool for monitoring a potential cyclical upswing or downswing in real time.

How Pronounced? The Six-Month Smoothed Growth Rate

Cyclical changes tend to be pronounced in magnitude, compared with noncyclical blips, or noise. But how do we measure whether a change is pronounced?

The most common measures of the magnitude of change are the month-to-month change and the same-month-year-ago comparison. The former yields relatively noisy series, and for this reason many practitioners prefer the latter.

The same-month-year-ago comparison was originally a device used to minimize seasonal distortions before the widespread use of seasonal adjustment procedures. For seasonally adjusted series, the remaining advantages of this measure, apart from simplicity, are few.

On the contrary, this measure has major drawbacks, which can be critical at cyclical turning points. For example, "when a cyclical decline occurs, it usually takes a continuation of the tendency for several months before a decline below the same month of the year before becomes apparent.... [I]n case of a smooth symmetrical cycle, same-month-year-ago comparisons...will show turning points six months late. In other, asymmetrical, types of cycles, the timing can be as much as eleven months too late" (Shiskin, 1961). Similar criticism had been leveled at the measure decades earlier (Macaulay, 1931).

Also, for a noisy series, such a measure can introduce major distortions. "Thus figures for a few months dominated by a strike may be divided by those for a few months dominated by abnormal weather, and the result could be almost anything" (Shiskin, 1961).

Why, then, is this twelve-month change measure still so popular? Perhaps the reason is just its simplicity, and the lack of well-known alternatives.

A superior measure introduced by Geoffrey H. Moore (1982a), and used extensively by him and his colleagues for many years for cyclical analysis, is the six-month smoothed growth rate, sometimes called the six-month smoothed annualized rate (SMSAR). The SMSAR [S.sub.t] of a time series [X.sub.t] is defined as follows:

[S.sub.t] = 100([X.sub.t]/[(([summation of][X.sub.t-i] where i=1 to 12)/12)).sup.(12/6.5)] - 100

This is really not as complex as it may first appear. All that [S.sub.t] represents is the ratio of the latest (monthly) observation in the time series [X.sub.t] to its average over the preceding twelve months, raised to the power of (12/6.5) to annualize the growth rate, then multiplied by 100 and 100 subtracted from that to express it as a percentage change.(1)

Because the twelve-month average in the denominator is centered 6.5 months before the current month, the ratio yields the change over a 6.5-month period. To obtain the annualized compound rate, the ratio is raised to the (12/6.5) power.

This measure has a number of advantages:

1. The denominator is smoothed over twelve months, so it is not affected very much by any unusual distortions in any particular prior month as the twelve-month change may be, i.e., the random element in the base from which the change is measured is reduced (Hiris, 1992).

2. Because the change measured is roughly over a six-month period rather than a twelve-month span, it reflects a cyclical upswing or downswing more promptly than the twelve-month change measure can. In spite of these advantages, the SMSAR is not any noisier than the twelve-month change and is certainly much smoother than the one-month change.